Clarification on how old the Universe is

[amorphos_b]

TL;DR Summary

a laymans inquiry because it seams it doesnt add up.

some data that you already know, just to get us started. i have tried to keep it as simple as i can...

The average distance between galaxies is about one million light years. There are roughly 100 billion galaxies in the observable universe.

https://aip.scitation.org/doi/10.1063/9780735421141_001

A light-year is equivalent to about 9.46 trillion killometres.

https://en.wikipedia.org/wiki/Light-year

individual galaxies typically move through space at relatively slow speeds: between 0.05% and 1.0% the speed of light, no more

https://www.forbes.com/sites/starts...-at-faster-than-light-speeds/?sh=5768e3d872a2

This means that for every megaparsec -- 3.3 million light years, or 3 billion trillion kilometers -- from Earth, the universe is expanding an extra 73.3 ±2.5 kilometers per second. The average from the three other techniques is 73.5 ±1.4 km/sec/Mpc.https://www.sciencedaily.com/releases/2021/03/210308165239.htm----------------------------------------------------------------------------------------------------------------------

so the average distance between galaxies is 1 million times 9.46 trillion miles. Then there are 100 billion galaxies. So if we drew a virtual line from anywhere e.g. planet earth, and extend it in any direction, there would be a massively further distance across the galaxies along that line, e.g. than that the universe is thought to be! - 13.7 billion years old. That’s just isn’t very old at all in cosmological terms.
In fact we should gather the averages from all the galaxies and not just along a virtual line.
So how old is the universe?

If we are looking at the age of the oldest light we can currently see, such to get the number 13.7, then that is surely a faculty of light. We can only look so far back into light before it becomes unpassable and uniform [background radiation].
What does it mean if the universe is older [or much older like a trillion years old or something] than the light we are reading? That there are more galaxies all in different positions than we thought?
Is it a faculty of light that it becomes more uniform the further we look into space and into the past? Then that at uniformity we cannot see any further, and yet if the universe is older than the light, then there is something further than the background radiation.
Is it then that the light is changing and becoming more uniform, but the universe itself is not. At least if the universe is older than the light we see, then the universe is not on the same curve as the light?

 

[Ibix]

If there are 100 billion galaxies in the universe and we assume an even spacing of galaxies, then the observable universe is roughly 4,600 galaxies across (the number in the volume being the cube of the number on a side). Taking your number of million light years between galaxies, that makes an estimate of the distance across the observable universe of about 4.6 billion light years, or a radius of 2.3 billion light years. That's a lot less than the actual distance to the edge of the observable universe, which is about 45 billion light years.

So none of the numbers you cite are inconsistent with an age of the universe of 13.7 billion years. The difference between the naive estimate of a 2.3 billion light year radius and the "official" 45 billion is most likely because galaxies aren't uniformly distributed in a grid, but concentrated in filament structures at the edges of voids. That would make the naive estimate an underestimate (as, indeed, it turns out to be).

I suspect you forgot to take the cube root of the number of galaxies in the observable universe when you were estimating the radius. That would give you an absurdly large number, but very wrong. Your speculation is, therefore, baseless.

 

[Ibix]

Here's why you should have taken the cube root:

That's 27 "galaxies" filling a volume. The distance across the group of galaxies is not 27 times the distance between two galaxies. The number you should be interested in is the cube root of 27, which is 3 - as you can see from the image.

 

[amorphos_b]

this is why i went along a single virtual line - so i am visualising one galaxy after the other.

I think it is the speed of expansion I am mostly confused by; if a car moves at 100 mph in one direction and another at the same speed in the opposite direction, their overall speed is 200 mph.If the cars were photons traveling at the speed of light, they cannot go faster than the speed of light, which means they are traveling at half the speed of light?

it seamed like the distances between galaxies just along a line made the age of the universe much more.

Sorry, I did say a laymans conception didn’t I lol

 

[Ibix]

this is why i went along a single virtual line - so i am visualising one galaxy after the other.

Yes. So (naively) there are only 4600 in that line, and no shortage of volume.

I think it is the speed of expansion I am mostly confused by; if a car moves at 100 mph in one direction and another at the same speed in the opposite direction, their overall speed is 200 mph.If the cars were photons traveling at the speed of light, they cannot go faster than the speed of light, which means they are traveling at half the speed of light?

You have several different errors here.

First, the expansion of the universe doesn't have a speed, it has a rate. Something that is now two billion light years from us is receding twice as fast as something one billion light years away - so there isn't a single speed, just a rate at which the recession speed increases as you go further away.

The rest of the part of your post I quoted is confusing "separation rate" and "relative speed". The two concepts are the same in Newtonian physics, but not in relativity. Yes, if I stand by the side of the road and two cars travel in opposite directions along the road at 100mph I will measure the distance between them to shrink (or grows) at 200mph - this is "separation rate". However, if one driver measures the rate at which the other car approaches they will find it to be slightly less than 200mph, by around 1 million millionth of a mile per hour - this is "relative speed". The difference is an effect of relativity, and the smallness of the figure is why we didn't notice for so long. If the cars are replaced by something doing a substantial fraction of the speed of light then the difference is much larger. In summary, I can measure two things closing on each other at speeds of up to 2c, but they will never measure the other to be traveling faster than c.

Finally, note that the cars cannot travel at c - only massless objects like light can travel at c. It isn't even possible to discuss cars traveling at c in principle, as it leads to self-contradiction.

 

[kimbyd]

If there are 100 billion galaxies in the universe and we assume an even spacing of galaxies, then the observable universe is roughly 4,600 galaxies across (the number in the volume being the cube of the number on a side). Taking your number of million light years between galaxies, that makes an estimate of the distance across the observable universe of about 4.6 billion light years, or a radius of 2.3 billion light years. That's a lot less than the actual distance to the edge of the observable universe, which is about 45 billion light years.

So none of the numbers you cite are inconsistent with an age of the universe of 13.7 billion years. The difference between the naive estimate of a 2.3 billion light year radius and the "official" 45 billion is most likely because galaxies aren't uniformly distributed in a grid, but concentrated in filament structures at the edges of voids. That would make the naive estimate an underestimate (as, indeed, it turns out to be).

I suspect you forgot to take the cube root of the number of galaxies in the observable universe when you were estimating the radius. That would give you an absurdly large number, but very wrong. Your speculation is, therefore, baseless.

There's also two other facts that are important here:
1) Galaxies very far away were too dim or too redshifted to be observed when that 100 billion number was coined (If I remember correctly, this came from the Hubble Ultra Deep Field). We only saw either the very bright ones or the more nearby ones. I believe current estimates of the number of galaxies visible from Earth are much higher.
2) As we look further away, we look back in time. Further than a certain point, galaxies will not have even formed yet. So we should expect the "visible distance" from this estimate of typical galaxy distances to be smaller than the observable distance.

I'm not sure that clustering has a very large impact on this measure, because the average distance between galaxies in two different clusters is large while those within clusters is small, so that it should largely balance out. The typical nearest-neighbor should be a much smaller distance than the average distance between galaxies.

 

[Ibix]

The typical nearest-neighbor should be a much smaller distance than the average distance between galaxies.

I'm not sure at all what it means by "average distance between galaxies" if it doesn't mean something like "average nearest neighbour" or maybe "average separation in clusters". The average distance between this galaxy and all other observable galaxies ought to be a sizeable fraction of the radius of the observable universe.

It does seem large for a nearest neighbour distance, though, agreed. Andromeda is only about 150 thousand light years away, barely a sixth of the quoted figure.

 

[Bandersnatch]

150 thousand light years away

Off the top of me head, 2 million, more like.

 

[Ibix]

Off the top of me head, 2 million, more like.

Oops! You're right - I read the diameter instead of the distance...

 

[Baluncore]

The average distance between galaxies is about one million light years. There are roughly 100 billion galaxies in the observable universe.

The pitfall with doing something like estimating the age of the universe, is that you must study the fundamental source of every number you use as input. For example, the average distance between galaxies you used, may have been estimated based on an assumed age and size of the universe. So you may find that your estimate is self-referential, you are simply checking someone else's arithmetic.

Once you have fixed the dimensions of the geometry, and the arithmetic, the closer your estimate is to 13.7 Ga the more suspicious you should be, that you have a circular argument.

 

[phyzguy]

Is it a faculty of light that it becomes more uniform the further we look into space and into the past? Then that at uniformity we cannot see any further, and yet if the universe is older than the light, then there is something further than the background radiation.

I think the other posters have not answered this question. There is no such property of light that makes it become more uniform as we look further into space and back into time. The reason the cosmic background radiation is so uniform is that the universe was very uniform at the time the cosmic background radiation was emitted. It was very much more uniform than it is today.

 

[amorphos_b]

thank you all very much!